


91 
n75 C7 
^ 1916a 
Copy 1 



T'Ae Relation of Inference 
to Fact in Mill's Logic 

By 
/.. FORSYTH CRAWFORD 



PHILOSOPHIC STUDIES 

ISSUED UNDER THE DIRECTION OF THE DEPARTMENT OF 
PHILOSOPHY OF THE UNIVERSITY OF CHICAGO 

NUMBER 5 



THE UNIVERSITY OF CHICAGO PRESS 
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THE MARUZEN.KABUSHIKI.KAISHA, Tokuo, Osaka, Kyoto 

KARL W. HIERSEMANN. Leipzig 

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The Department of Philosophy of the University of Chicago issues 
a series of monographs in philosophy, including ethics, logic, and meta- 
physics, aesthetics, and the history of philosophy. The successive 
monographs are numbered consecutively with a view to their subsequent 
publication in volumes. These studies are similar to the series of 
Contributions to Philosophy, but do not contain psychological papers or 
reprints of articles previously published. 



THE RELATION OF INFERENCE TO FACT 
IN MILL'S LOGIC 



THE RELATION OF INFERENCE TO 
FACT IN MILUS LOGIC 



/ BY 



J^ FORSYTH CRAWFORD 




THE UNIVERSITY OF CHICAGO PRESS 
CHICAGO, ILLINOIS 

iVionograph, 



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Copyright iqi6 By 
The University of Chicago 



All Rights Reserved 



Published April 1916 



Composed and Printed By 

The University of Chicago Press 

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APR 28 1916 



lU 



CONTENTS 

CHAPTER PAGE 

I. Subjective Facts as Data 7 

II. The World of Objective Facts 16 

III. The Universality of Attributes aistd PROPOSiTioisrs . . .22 

IV. Inference as Anticipation of Facts 27 

V. Inference as Proof of Propositions 34 

VI. Inference as Discovery 43 



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CHAPTER I 

SUBJECTIVE FACTS AS DATA 

The problems of logic are coming to form the center of interest in 
philosophical discussion. Most present controversies in the field of 
philosophy turn upon some difference which is fundamentally logical. 
There is need, therefore, to re-examine and clarify the underlying con- 
ceptions of logic. Any one of the great historical systems of logic offers 
a species of laboratory example of the shaping of logical concepts under 
some specific point of view, and the difficulties which it leaves unresolved 
offer valuable experimental material for further logical construction. It 
is with such a purpose that this paper undertakes an analysis of the 
relation of inference to fact in Mill's logical system. 

In constructing a theory of inference Mill's problem was to reconcile 
the associationism of the English empirical school with the procedure of 
modern physical science. He occupies alternately the subjective point 
of view of the one position and the objective point of view of the other. 
This oscillation of position comes out strikingly in the varied status 
which he gives to facts, which are at one time the ultimate constituents 
of consciousness and at another time the things and events of an inde- 
pendent world. When stating the relation of inference to its data and 
thus assigning it a locus, he takes the subjective point of view. When 
analyzing the nature of inference and basing its validity, he takes the 
objective point of view. It will be well, then, at the outset, to examine 
his conception of both subjective and objective facts, and the transition 
which he seeks to effect from the one to the other. Over against both 
of these, facts in the mind and facts in nature, Mill naively utilizes a 
system of meanings which he never thinks of as sundered from the facts, 
yet which are assumed as logically independent in his inferential process. 
An examination of the system of meanings we shall postpone till after 
we have examined his assumption of facts, and will consider the latter 
apart from their meaning so far as that can be done without distortion. 

The locus of inference in relation to fact, as assigned by Mill, rests 
on the distinction between immediate and mediate knowledge. The 
first is self-evident, the second reasoned. We obtain the first by intui- 
tion, the second by inference. "Truths are known to us in two ways: 
some are known directly, and of themselves; some through the medium 

7 



8 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

of other truths. The former are the subject of Intuition; .... the 
latter, of Inference." '■ They are " truths known to us by immediate con- 
sciousness" and "conclusions which can be drawn from these. "^ Of these 
two classes of truths, the first does not require proof; such a truth carries 
its own evidence — "that is, is without evidence in the proper sense of 
the word."^ It must therefore be "known beyond possibility of ques- 
tion."-* One cannot but be certain of it. But only a small part of our 
knowledge has intuitive character.^ By far the larger portion hangs 
suspended from these immediate truths by a series of proofs. 

This apportionment of knowledge appears on the face of it very clear 
and definite. At any rate it seems to offer a hopeful program: to begin 
with perfectly certain data and to let each step from those data be one 
of strict proof. Upon examination, however, the simplicity of the matter 
disappears. Like the gratuitous advice to "be sure you are right, then 
go ahead," this program does not tell us how to know when we are right. 
This conception of primitive and unquestionable data, indeed, is thor- 
oughly ambiguous. While he does not uncover its source. Mill has to 
acknowledge this ambiguity in two respects: 

First, Mill admits that there is difference of opinion as to the kind 
of data from which we start. He sets in sharp contrast two theories on 
this point: the "ontological" theory of the Scotch school, and the 
empirical theory of his own English predecessors, which he defends.^ 
The former holds that, in addition to the data admitted by the latter 
school, the mind is so constituted as to know intuitively the existence and 
laws of operation of certain objects external to the mind, while the latter 
recognizes "no ultimate premises but the facts of our subjective con- 
sciousness; our sensations, emotions, intellectual states of mind, and 
volitions." Mill considers all thinkers to be agreed that there are some 
such primitive data, but to disagree as to whether or not such data are 
exclusively subjective. But surely the very possibility of dispute as to 
the character of what are to be considered primitive data is a very 
serious obstacle to the theory that there are any data at all to be taken 
as unambiguously primitive. 

There is a second ambiguity of more serious character, not so expli- 
citly recognized, though virtually acknowledged by Mill. While it 

' Mill, Logic, 8th ed., Harper, igd. References to the Logic are hereafter by page 
numbers, without repeating the title. To make references to the Logic more definite, 
letters are added to designate in order each paragraph or part of paragraph on a page. 

^ ige-2oa; Mill, Examination of Hamilton, 137. 

3 216. < 20c. s 21C. ^ 5206. 



SUBJECTIVE FACTS AS DATA g 

seems clear to him that consciousness immediately reveals the primitive 
data of our knowledge, which consist of our own subjective states, Mill 
finds it impossible in practice to determine what those data are. Assum- 
ing agreement as to their subjective character, their actual discovery in 
detail proves impossible. Supposed to be known "beyond the possi- 
bility of question," they are in fact unrecognizable, because they cannot 
be distinguished from the inferences that are drawn from them. "We 
may fancy that we see or feel what we in reality infer. A truth, or a 
supposed truth, which is really the result of a very rapid inference, may 
seem to be apprehended intuitively."' Observation, which is another 
name for intuition, is constantly vitiated by confusion with inference. 
"Observation and inference are intimately blended."^ Now if we ever 
mistake inference for observation, it surely follows that we can never be 
sure we have not done so. There is no safe criterion by which to dis- 
tinguish the two; for the apparent self-evidence of immediate intuition, 
our only resource in the case, is admitted to be liable to fail. It is idle 
to urge "a correct discrimination between that, in a result of observa- 
tion, which has really been perceived, and that which is an inference from 
the perception,"^ for the supposed purity of the observation may still be 
only our "fancy." "From my senses," Mill claims, "I have only the 
sensations, and those are genuine."'' No doubt they would be genuine 
if I could be sure that they are truly mere sensations. " Errors of sense," 
he says again, "are erroneous inferences from sense; .... the decep- 
tion .... is in my judgment. "^ But since such errors are always 
possible, how can I know that there are no further errors of judgment 
lurking in what I fancy to be perception ? 

Evidently this distinction between intuition and inference proves 
unworkable, and breaks down for lack of a criterion of discrimination 
between the two. If we press the difficulty farther to discover its precise 
nature, we find it involved in Mill's theory of consciousness, or of expe- 
rience, as consisting of given mental states. An experience of that kind 
would properly leave no room for inference; and in grafting inference 
upon it Mill introduces an alien element in contradiction with his 
premises. This point will repay closer examination. 

' 2od. Cf. Mill, Berkeley, 278. 

* 4506. So Mill contrasts "experience" with "a mistaken supposition of experi- 
ence" (iQsd), or with "a superficial semblance of experience" (196a). 

5451C. "We ought to know what part of the assertion rests on consciousness, 
and is therefore indisputable, what part on inference, and is therefore questionable" 
(S4Sc)- 

''4Si<i- 5 4SO<^- 



10 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

Mill professes himself an adherent of Berkeleyan idealism, which he 
received from his father in the form of an elaborated associational psy- 
chology. To this school of thinkers it seems axiomatic that only our 
own mental states are immediately known to us. It inevitably follows 
that consciousness is shut up to its own subjective contents, and that 
the knowledge of anything else, if the possibility of such knowledge be 
granted, must be capable of translation into terms of mental states. 

The primary interest of this school, both historically and construct- 
ively, is directed upon the analysis of the knowledge of an external 
world into constituents of sensation. So strong is this interest in sen- 
sation, an interest which has rightly earned for the school the designation 
of sensationalist, that one would almost suppose consciousness to be 
composed solely of a kaleidescopic succession of sensations. Sensations, 
in their temporal and spatial discreteness, their qualitative resemblances, 
and their associational connections, are at any rate taken as the type 
of mental facts. And it is this sensationalism on which Mill rests when 
he lays down the distinction between intuition and inference. 

Yet sensations are not the only contents of the mind acknowledged 
by Mill. With reference to the other contents of the mind there are two 
conflicting tendencies: either, on the one hand, to reduce them all to 
mere given mental states of the same immediacy as sensation, in which 
case there is no opening for inferences to slip between them; or, on the 
other hand, to lift them to the level of various operations performed upon 
and with sensation, in which case inference finds a work to do but 
immediacy is gone. 

There are several of these other classes of mental states recognized 
by Mill, and one or two factors that he does not think of classing as 
mental states, but which, if not so classified, do not fit into his original 
theory of consciousness. Beside sensations, he classes as mental states 
images, emotions, volitions, and thoughts. Relations he hesitates about 
so classing. Meanings he does not class here, and on this side of his 
system they are simply an outstanding factor. Some of these non- 
sensational mental facts require examination. 

What we now call mental images constitute the simplest of the non- 
sensational mental states recognized by Mill. Mill usually calls them 
"ideas," as against sensations, which he also calls "impressions," after 
Hume.' "Whenever any state of consciousness has once been excited 
in us, no matter by what cause, an inferior degree of the same state of 
consciousness, a state of consciousness resembhng the former, but 

' But of course he has other uses of the term "idea." 



SUBJECTIVE FACTS AS DATA ii 

inferior in intensity, is capable of being reproduced in us without the 

presence of any such cause as excited it at first This law is 

expressed by saying, in the language of Hume, that every mental impres- 
sion has its idea."^ "These ideas, or secondary mental states, are 
excited by our impressions, or by other ideas, according to certain laws 
which are called Laws of Association."^ Here one might be tempted to 
see between primary and "secondary mental states" a distinction cor- 
responding to that between intuition and inference, or immediate and 
mediate. But such a comparison would be entirely misleading. Impres- 
sions and ideas stand for Mill upon exactly the same level of immediacy. 
The distinction which he makes between them on the ground of the 
presence or absence of a stimulating object^ is from this point of view 
illegitimate, for it is not based on a difference in their actual analyzable 
content, but is itself an inference we draw from their organized relations. 
Again, the laws of association by which these secondary states are aroused 
by no means coincide with the inferential laws by which we pass from 
facts directly known to facts known through proof. The confusion of 
inference and association which sometimes does arise Mill expressly 
brands as a serious logical fallacy.'' Sensations and images, in short, are 
on the same level of immediacy, both directly given in consciousness. 
They are both mental fact. From this point of view we should have 
no right to treat memory and expectation as in any sense a means of 
rising inferentially above the immediate data of consciousness. 

The other mental states which must be included in the immediate 
content of consciousness Mill classifies as thoughts, emotions, and 
volitions. These are taken exactly in the same way as sensation, all 
equally immediate. Emotions and volitions^ we may for our present 
purpose lay aside. But the mental states which he calls thoughts have 
grave significance for a theory of inference. 

It is certainly disconcerting to find the class of "thoughts" included 
as a member of this list. Where is inference to come in if it is not 
thought? But thoughts too are taken as mere mental facts. "Under 
the word Thought is here to be included whatever we are internally 
conscious of when we are said to think."^ These "intellectual states of 

' SQii. ^ S92a. 3 591^^. 

'• 521-23, and elsewhere. 

s A volition indeed is made up of two things: a physical efiect, preceded by a 
"state of mind"; the latter is the "intention to produce the effect," and that belongs 
to the content of consciousness (516). 



12 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

mind" are just as primitive and immediate facts as sensations, for Mill 
"recognizes no ultimate premises but the facts of our subjective conscious- 
ness: our sensations, emotions, intellectual states of mind, and volitions."^ 
We are here confronted with a curious and most significant difficulty, 
which brings into question the whole doctrine of immediacy in Mill's 
sense. For certainly inferences, knowledge obtained by reasoning, not 
only what we see and feel but what we "fancy that we see or feel," are 
all in some sense "intellectual states of mind"; they are part of what 
"we are internally conscious of when we are said to think." Yet this 
thinking, which is surely to be set in contrast with the data of inference 
as the very process of inference if there is such a thing as inference at all, 
is in turn swept back into the contents of consciousness, all of which are 
immediately given as the data of inference. The immediacy of all mental 
states and the genuineness of inference are thus in flat contradiction. 

In the next place, how does Mill treat relations ? Between facts of 
nature, taken in the objective sense that will come before us below, Mill 
recognizes the possibility of all sorts of relations; but these are all 
reducible to the subjective relations of coexistence, succession, and 
resemblance between mental states, and it is the latter that concern us 
here. Here we meet with the same ambiguity. Mill wavers between two 
positions. For these relations between objective facts are reduced sub- 
jectively either to relations between states of consciousness or to states 
of consciousness themselves. On the one hand, " those relations, when 
considered as subsisting between other things, exist in reality only 
between .... states of consciousness";^ on the other hand, "there is 
no part of what the names expressive of the objective relation imply 
that is not resolvable into states of consciousness."^ The peculiar sig- 
nificance of this ambiguity lies here, that only when these relations are 
taken as themselves states of consciousness can they be treated con- 
sistently with Mill's general theory of the subjective immediacy of con- 
sciousness; while only as they are treated as somehow different from 
states of consciousness, added to them, as it were, or involving reorgani- 
zation of them, is there room for a process of inference that, while resting 
on immediate intuition, shall build upon it a structure of mediated 
knowledge. The ambiguity is indispensable to the seeming clearness 
of the original distinction between intuition and inference. So we find 
Mill asserting on the one side that "resemblance is nothing but our 
feeling of resemblance; succession is nothing but our feehng of succes- 

' 520& (italics mine). 

2 65g (italics mine). ' 606 (italics mine). 



SUBJECTIVE FACTS AS DATA 13 

sion"^; and on the other side that "our consciousness of the succession 
of these sensations is not a third sensation or feeling added to them."^ 
Mill simply assumes that, because "to have two feelings at all impHes 
having them either successively or else simultaneously," therefore suc- 
cessive sensations are somehow a sensation of succession; and so with 
the other relations. How this can be is well acknowledged to be a 
mystery. "These feelings of resemblance and .... dissimilarity are 
parts of our nature; .... states of consciousness which are peculiar, 
unresolvable, and inexplicable. "^ They are "either .... states of 
feeling, or something inextricably involved therein."'' 

The final breakdown of this doctrine of immediacy of consciousness 
is disclosed when a system of meanings is set up over against the merely 
passing, given facts. But it will be convenient to postpone a discussion 
of Mill's system of meanings till after we have examined his attempt to 
build objective out of subjective facts. We may then be able to trace 
more clearly the root of Mill's difficulty. But it is already evident that 
there is a confusion in Mill's conception of given mental facts. Indeed, 
it appears to involve three distinct errors, perhaps all cardinal errors of 
the associational school: 

First, all analyzed content of experience is made subjective. The 
unavowed motive for this is probably as follows: The strain of attention 
required to analyze any content of experience, and the temporary uncer- 
tainty as to the outcome of the analysis, are used as indications that the 
content when so analyzed is subjective.^ The effort, for example, to 
distinguish the baffling shades of green seen upon a meadow, or the evan- 
escent chirps and hums heard in the same meadow, acts as a motive to 
refer back to subjective consciousness the colors and sounds when they 
are discriminated. In this way all phenomena when analyzed tend to 
become psychological, and experience is taken as composed of mental 
states. 

Secondly, these subjective products of analysis are then regarded as 
genetically prior to the analysis which brought them to consciousness. 
Because they are now found there, it is supposed that they must pre- 
viously have been there.^ An experience which analytic attention has 
succeeded in differentiating into elements is taken as having been pre- 
viously constructed by an association of similar elements. So the course 

^ 636. ^ 60c. 3 6iffl. 4 656. 

s Mead, "The Definition of the Psychical," University of Chicago Decennial 
Publications, First Series, III, 23-38. 

^ Royce, Outlines of Psychology, 97-117, has an excellent discussion of this fallacy. 



14 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

of experience becomes an agglomeration of original, subjective, internally- 
fixed units. This is sensationalism combined with associationism. 

Thirdly, a succession of logically independent units is expected to 
constitute a single experience. Mental states as mere facts are wholly 
evanescent, and are never repeated. How then can there be any accu- 
mulation in the series ? At times Mill is fully aware of the difficulty, and 
acknowledges as inexplicable the power possessed by the series of mental 
states of knowing itself as a series.^ But this inexplicability never drives 
him back to a reconsideration of his first assumption. Leaving the 
mental facts in their bare givenness and independence, he naively adds 
to them an "impulse of the generalizing propensity."^ Now Mill is of 
course right in regarding generalization as most significant for the theory 
of inference. The whole possibility of inference to reach after and before 
rests on generalization. But the propensity to generalize is a somewhat 
startling addition to the scheme of simply associated mental states. Is 
it not in fact a contradiction ? Given a succession of barely presented 
mental contents, one can suppose an addition of more such contents and 
more varied contents. But how could generalization get any foothold 
among them? What could generalization possibly mean in terms of 
such contents, even including immediate feelings of resemblance ? The 
truth is that Mill has assumed, side by side with his system of mental 
states, a system of universal meanings. Were it not for these, inference 
could be only the piling up of more intuitions. With them, inference 
finds expression in significant propositions. The mysterious propensity 
of the mind to generalize is simply the illicit acknowledgment, whenever 
they are needed, of a system of meanings which connect the bare, passing 
facts of consciousness and elevate them into an organic experience. 

To recapitulate. Mill starts with a sharp distinction between imme- 
diate intuition and mediate inference. The distinction, however, breaks 
down, because if the given facts of consciousness are made to include all 
the contents of experience there is no room for inference, while if we 
allow an element of inference in some of the facts of constiousness any 
facts may be equally infected and no data are left whose immediacy can 
be guaranteed. Mill escapes the pressure of the difficulty only because 
his treatment of inference is disrupted into two parts: On the subjective 
level he assigns the locus of inference by asserting its distinction from 
intuition; but he does not on this level discuss the method of inference, 
and so escapes the need of a criterion of its distinction from intuition. 

' Mill, Examination of Hamilton, I, 260-62. 
^ lS'^d, 227a, h. 



SUBJECTIVE FACTS AS DATA 15 

On the objective level he elaborates a method of inference, but the imme- 
diate data upon which the method must operate he assumes as already 
provided on the subjective level. On the one level everything is datal, 
with no room for inference; on the other, there is a method of inference 
but no starting-point for its operation. This last assertion can receive 
its justification, however, only after an examination of Mill's treatment 
of objective facts, to which we may now turn. 



CHAPTER II 
THE WORLD OF OBJECTIVE FACTS 

The world of facts with which Mill's inferential process actually deals 
is a thoroughly objective world, conceived in terms of pure naturalism; 
not at all the world of subjective mental facts which he first assumed. 
When Mill is expounding its method it is these objective facts upon 
which inference is made to rest. 

How does Mill reach this world of objective facts? Ostensibly he 
gets it by a process of complication of the associative connections of 
mental states. The complications become so involved that the original 
mental states drop out of sight and the complications alone remain, to 
form an objective world of things and events. It would be aside from 
our purpose to criticize this transition in detail, but we may note three 
fundamental characters of the objective world thus reached by Mill. A 
statement of these will make clearer the nature of the shift from a sub- 
jective to an objective level. It will then also be observed that they 
correspond closely to the three "analogies" of Kant. 

In the first place, it is a world of things, existing permanently and 
independent of individual consciousness. The transition to this concep- 
tion from that of mental states is effected by means of the conception of 
permanent potentialities of sensation.^ On the Berkeleyan level, where 
experience of objects is interpreted in psychological terms, sensible things 
are sensations, and the existence of sensible things means their perception 
by the mind. Nature is but the aggregate of sensible ideas, and the 
uniformity of nature is a uniformity in the order of sensations. Now 
Mill, as we have seen, starts on this level; but by means of complicating 
associations he rises to an objective level, on which the permanent poten- 
tialities of sensation serve as a core around which phenomena are organ- 
ized.^ Substance is thus conceived as a fixed group or set of potentialities 
of sensation joined together according to a fixed law. These are not 
"mere vague possibilities," but "conditional certainties. "^ They are 

' This transition is briefly described in the Logic, 53-54. The classical passage 
in which it is elaborated is in Examination of Hamilton, chap. xi. In both these works 
Mill uses the term "possibilities of sensation." In his later Essay on Berkeley he uses 
the more appropriate term "potentialities." 

^ Logic, 4516, 4561;, 4256-2611. 3 Mill, Hamilton, 238. 

16 



THE WORLD OF OBJECTIVE FACTS I^ 

considered objective because of their permanence, their rehability, and 
their social community. First, they are permanent. "The conception 
I form of the world .... comprises, along with the sensations I am 

feeling, a countless variety of possibilities of sensation These 

various possibilities are the important thing to me in the world. My 
present sensations are generally of little importance, and are, moreover, 
fugitive; the possibilities, on the contrary, are permanent, which is the 
character that mainly distinguishes our idea of Substance from our 
notion of sensation."^ The object is "invested with the quality of per- 
manence, in contrast .... with the temporary character of each of the 
sensations composing the group " ;^ it "presents itself to the mind . . . . 
as a kind of permanent substratum, under a set of passing experiences or 
manifestations." "The whole set of sensations as possible, form a per- 
manent background to any one or more of them that are, at a given 
moment, actual."'' Secondly, they are reliable even when they pass out- 
side the individual's experience.'' "The reliance of mankind on the real 
existence of ... . objects, means reliance on the reality and perma- 
nence of Possibilities of ... . sensations, when no such sensations are 
actually experienced. "^ "Our sensations v/e carry with us wherever we 
go, and they never exist where we are not; but when we change our place 
we do not carry away with us the Permanent Possibilities of Sensation; 
they remain until we return, or arise and cease under conditions with 
which our presence has in general nothing to do."^ Thirdly, they are 
socially common. For "more than all .... they are, and will be after 
we have ceased to feel. Permanent Possibilities of Sensation to other 
beings than ourselves." "The permanent possibilities are common to 
us and to our fellow-creatures: the actual sensations are not." "The 
world of Possible Sensations succeeding one another according to laws is 
as much in other beings as it is in me," "it has therefore an existence 
outside of me; it is an External World." "This puts the final seal to 
our conception of the groups of possibilities as the fundamental reality 
in Nature."^ For such reasons as these "our actual sensations and the 
permanent possibilities of sensation, stand out in obtrusive contrast to 
one another"; and " the possibilities .... come to be looked upon as 
much more real than the actual sensation; nay, as the very realities of 
which these are only the .... appearances."^ 

' Ibid., 237; Berkeley, 279-81. ■* Logic, 425c, d. 

' Mill, Hamilton, 239. ' Mill, Hamilton, 244. ' Mill, Hamilton, 242. 

^ Ibid., 2^1. ^ /JiW., 249-50. ^ Ibid., 240. 



i8 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

These groupings in nature, then, no longer subsist for Mill immedi- 
ately between mental states as such, but are composed of mental states 
only remotely or indirectly. When we once get them we forget their 
associational origin and treat them in an entirely naturalistic fashion. 

In the second place, the relation of cause and effect holds, not of sen- 
sations directly, but of these objects. Precisely as substances are lifted 
from groups of sensations to an objective level, so causal connections 
between these substances come to replace mere associations between 
sensations.^ "In addition to fixed groups, we also recognize a fixed 

Order in our sensation Now, of what nature is this fixed order 

among our sensations ? It is a constancy of antecedence and sequence. 
But the constant antecedence and sequence do not generally exist between 

one actual sensation and another In almost all the constant 

sequences which occur in Nature, the antecedence and consequence do 
not obtain between sensations, but between the groups we have been 
speaking about, of which a very small portion is actual sensation, the 
greater part being permanent possibilities of sensation. Hence, our 
ideas of causation .... become connected, not with .... our sensa- 
tions as actual at all, .... but with groups of possibilities of sensa- 
tion."^ 

When this conception of causal laws has been obtained it is supposed 
to be carried to the farthest limit of generalization, and is treated as an 
absolute character of the objective world. Every event takes place 
according to a fixed law of sequence, and the whole universe is law- 
abiding. Mill attempts to deduce this causal character of the whole 
course of the universe, somewhat as he did its independent existence, by 
a complication of subjective association j^ but here even more obviously 
than there he must leap to another level before there is any place for the 

' Mill, Berkeley, 288. 

' Mill, Hamilton, 239-40. There is much confusion in Mill as to the place of 
sensation in the causal scheme. Objective things, as potentialities of sensation, 
apparently include all actual sensations as that part of their content which happens 
to be experienced. If so, how can sensations be given a place as distinct links in the 
causal series ? This is to duplicate them. This is similar to the difi&culty in Kant of 
referring sensations to things in themselves as causes of the sensations, although 
causation is properly a category only of the phenomenal world, which consists of 
objectively organized sensations. This confusion in Mill suggests the difficulty found 
by neo-reaUsts in assigning to consciousness a place in the realistic scheme. The 
following passages in Mill's Logic may be consulted in this connection (46a, 496, 51a, 
52e, 576, 636-64a, 816, 82c, 242b, 4516, sSgd-goa). 

' 397-405- 



THE WORLD OF OBJECTIVE FACTS 19 

conception of objective things and laws. Ostensibly a generalization 
from particular causal connections, it is taken as an absolute assumption 
by which each of them may be tested. 

That the two characters of the objective world already referred to 
are really assumptions independent of the subjective basis on which they 
are ostensibly grounded becomes all the more evident when we consider 
its third character, which is in a sense the limit to which the other two in 
combination are pushed. For, in the third place, Nature is taken as a 
single, unitary whole; its objects, through the interaction of their prop- 
erties, forming a completely interrelated system, whose operations are 
absolutely determined. "The state of the whole universe at any instant 
we believe to be the consequence of its state at the previous instant; 
insomuch that one who knew all the agents which exist at the present 
moment, their collocation in space, and all their properties, .... could 
predict the whole subsequent history of the universe." "The whole 
series of events in the history of the universe, past and future, is ... . 
capable, in its own nature, of being constructed a priori by anyone 
whom we can suppose acquainted with the original distribution of all 
natural agents, and with the whole of their properties."^ How remote 
is such a universe from an accidental agglomeration of given mental 
states! Mill has certainly passed here completely to an objective and 
universal level. 

Such is the naturalistic scheme within which Mill, when he presents 
the method of inferential procedure, looks for the data of inference. 
While we may find that it evinces internal difficulties which unfit it for 
this purpose, it certainly offers a sphere for the operation of inference 
very much more hopeful in appearance than that of immediate subjective 
states. The objective scheme which Mill has thus obtained bears a 
striking resemblance to that of Kant.^ The three features to which we 
have called attention correspond closely to the three analogies of Kant 

' 25oc-sia. 

^ Professor De Laguna, Dogmatism and Evolution, 179-82, calls attention to this 
resemblance, but in the main rejects it, on the grounds, first, that " the forms of con- 
nection which MiU considers .... are not intuitively known or assured," and 
secondly, that "it can never be asserted that a given description of any form of con- 
nection is adequate or final." But the general causal scheme, which is the factor in 
MUl corresponding to the Kantian categories, is taken as absolute. Kant, on the 
one hand, recognizes that specific causal laws must be learned from experience; while, 
on the other hand, the. form of connection, when Mill once gets it, operates in as abso- 
lute a sense in Mill as in Kant. It is "adequate" and "final." See such passages 
as 237a, 2Soc-sia, 34SC, and S47e-48a. 



20 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

as organizing principles for experience, and the correspondence can in 
fact be pointed out in considerably fuller detail than the present purpose 
will permit. Is this resemblance merely superficial, or is it significant ? 

There are of course obvious differences. Mill set out from an 
empirical standpoint, and intended to remain an empiricist. He repu- 
diated any contribution to experience by the structure of the mind itself, 
and tried, as we have seen, to trace the growth of even the most fixed 
forms of nature from the simplest associative connections. Certainly 
Mill did not mean to be a Kantian. Yet the resemblance is not without 
significance. Mill has moved a considerable part of the way from Hume 
to Kant. 

Hume and Kant both assume a congeries of mental states to start 
with. For both, these mental states are organized into objects. Kant's 
principles of organization are independent of the content; they are 
formal, contributed by the intelligence to the content. Hence the 
organization of the object has universality and necessity. Hume's 
principles of organization reside in the content, and are reducible to the 
principle of custom, or habit, which operates through contentual laws of 
association. Such organization of objects cannot have universality and 
necessity, for it rests on mere expectation, and the actual connections 
may change at any time. Change of organization, while it may surprise, 
does not rob the object of what for Hume renders it an object. Now 
what sort of organization of objects does Mill employ ? He starts with 
that of Hume, and avows it to the end. But after professing to deduce 
substance and causality as higher complications of empirical association 
(or habit based on mere empirical relations of content), he uses these 
objective principles of substance and causality (together with the prin- 
ciple of an absolutely reciprocal system of nature which he could not even 
profess to deduce by association) as though they were absolute principles 
which he can bring to the content of experience. Though he would 
never have avowed their seat in the constitution of the knower, he 
assumes their universality and necessity.' That is to say, he uses them 
just as Kant did. Kant had shown that universality and necessity of 
objects must be assumed independently of their content; and in uncon- 
scious accordance with this Mill assumes a universality and necessity 
that, as we have seen, could not have been properly reached by his asso- 
ciational construction of substance and empirical proof of causation. 
To be sure, Mill does not admit the conception of necessity; but he has 
a double use of the idea of universality, one of which amounts to the 

' Compare Joseph, Introduction to Logic, 376 ff. 



THE WORLD OF OBJECTIVE FACTS 2i 

same thing. That is universal in one sense which happens to be uni- 
formly experienced, and that is universal in another sense which is uni- 
form in nature whether experienced or not, and probably in no case 
unambiguously experienced; this latter cannot be distinguished from 
formal necessity. Indeed, Mill's unconditional universality,'' with its 
exclusion of transient force,^ is precisely Kant's necessity. His scheme 
of objective nature, then, is Kantian rather than Humian. 

The significance of this conclusion for our purpose lies in this, that 
the two modes of organizing experience allow a very different place for 
inference. Hume relies directly on custom, and gets no place at all for 
inference; mental states simply are or are not; they are all equally im- 
mediate. Kant relies not at all on custom, but believes himself to be in 
possession of a system of organizing principles independent of experience, 
which put objects into genuinely objective relations, and seem to make 
a place for inference regarding them. Now Mill holds substantially each 
of these positions in turn. He relies indirectly on custom, and so far as 
he does so has no place for inference, as we saw above; but when he has 
thus reached his objective principles of organization they then work 
with a universality unlike that of Hume and like that of Kant. Mill 
therefore is able to produce a logic which was impossible to pure associa- 
tionism. And his logic, in practically all of its actual construction, can 
be regarded as based on a purely naturalistic foundation. After once 
getting to the level where its procedure is worked out. Mill's logic is no 
longer sensational and associational, but realistic, and must be judged 
on that ground. One motive, it is true, among others in constructing 
his logic was to vindicate the associational philosophy by showing that 
a logic could be built upon it,^ but such a vindication would of course 
have to rest in part upon the cogency of the transition from the subjective 
to the objective level, as well as upon the adequacy of procedure of a 
quasi-realistic logic after the objective level has been reached. We have 
tried to show that the transition is not cogent. The difficulties of the 
realistic logic to which it leads Mill will appear below. 

' 244C-46C. 

^ 236^. 

3 Mill, Autobiography, 226. 



CHAPTER III 
THE UNIVERSALITY OF ATTRIBUTES AND PROPOSITIONS 

So far we have considered Mill's facts, whether subjective or objec- 
tive, as bare particulars. This is entirely fair to Mill's ofl&cial and 
avowed empiricism. But such facts would be of no service to the logi- 
cian; for they would be completely cut off from each other, giving no 
play for an interpretative process to bind them together. Facts as mere 
facts are never repeated. Mill accordingly imports into them a universal 
element by endowing them with attributes. This he does quite naively, 
not suspecting that in using attributes in a universal sense he has aban- 
doned his original attitude toward facts. 

We have already met with attributes in Mill's discussion of facts as 
the data of inference. We must now consider their function more par- 
ticularly. Attributes serve Mill in three ways: first, to reinforce the 
ultimate identity of subjective and objective facts; secondly, to furnish 
a bond of unity between facts; thirdly, to give content to propositions. 
This last function of attributes is consciously avowed by Mill; the 
service of the two former is somewhat surreptitious. 

In his use of the word attribute Mill glides from one meaning to 
another. At first the attribute is the quality of the sensation, already 
giving the sensation a universal aspect.^ The attribute is then trans- 
ferred to the thing, as the power the thing has of exciting a sensation.^ 
This mode of statement is first suggested very hesitatingly, but later 
accepted without reserve.^ The exciting of actual sensations at length 
falls out entirely, and attributes become the mere potentialities of causing 
them.'' The world of nature, with all its objective causal relations, can 
then be described as a realistic system in terms of attributes, now under 
the name of properties.^ Thus attributes carry Mill over by an easy 
transition from subjective to objective facts. 

Again, the attribute is the universal element needed by Mill to bind 
together his merely particular facts. Attributes give meaning to such 
facts precisely by their universality, and the particulars could get mean- 
ing in no other way. So Mill's doctrine of meaning is one of intention, 
not of extension. " We may frame a class without knowing .... any 



5 2506-5 la. 



57e, and many passages. 


3636. 


S7/-58ff, 58c. 


1860. 




22 



UNIVERSALITY OF ATTRIBUTES AND PROPOSITIONS 23 

of the individuals of which it may be composed; we may do so while 
believing that no such individuals exist. If by the meaning of a general 
name are to be understood the things which it is the name of, no general 

name, except by accident, has a fixed meaning at all The only 

mode in which any general name has a definite meaning, is by being a 
name of an indefinite variety of things; namely, of all things, known or 
unknown, past, present, or future, which possess certain definite attri- 
butes."^ This seems to give something very like a world of meanings 
over against a world of facts. The meanings are fixed in themselves, 
and it is a mere accident whether any corresponding particular exists or 
not. "General names .... have a meaning, quite independently of 
their being the names of a class. That circumstance is in truth acci- 
dental, it being wholly immaterial to the signification of the name whether 
there are many objects, or only one, to which it happens to be applicable, 
or whether there be any at all," " Every name the signification of which 
is constituted by attributes is potentially a name of an indefinite number 
of objects; but it need not actually be the name of any."^ It is quite 
true that Mill denies to these meanings an objective existence; attributes 
are not real things.^ Yet the meaning spills over the particular fact, and 
proves to be an identity above the particulars. Spencer criticizes Mill 
on this ground, charging him with confounding likeness of attributes and 
their identity. Mill rejoins that likeness of attributes is identity: "The 
common something which gives a meaning to the general name, Mr. 
Spencer can only say, .... is the similarity; .... and I rejoin, the 

attribute is precisely that similarity The things compared are 

many, but the something common to all of them must be conceived as 
one. "4 

Mill stands here in a position of unstable equilibrium. For him 
nothing but particular facts can be actual; his entire empiricism is here 
at stake. Yet the particular can be expressed in terms of attributes, and 
each attribute is identical, in however many facts. It is an absolute 
universal. Even further, as we have seen, an attribute need not actually 
imply a fact at all. The attributes as such, then, present a timeless 
system of characters without particularity. 

Mill here betrays the inevitable difficulty of assuming that particular 
facts are independent and isolated. This is due to a failure to realize 

' 78e (italics mine). 

^ 946. Cf. 84a. In neo-realistic terminology it may be the name of a subsist- 
ent, not an existent. 

3 1366. '' 137c; Spencer, Principles of Psychology, 125-27. 



24 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

that it is impossible to speak of particular facts without implying the 
presence of a person that has an interest in the facts, and to whom there- 
fore they are not mere particulars. Provisionally and for certain pur- 
poses, to be sure, it is necessary to treat facts as independent; but their 
independence is still the way they are being treated. The results of the 
logical process cannot be made valid in absolute independence of the 
interest in that process. An attribute is attributed. Particulars and uni- 
versals are strictly correlative. Any attempt to get a logic out of mere 
particulars therefore puts one under compulsion, whether surreptitiously, 
like Mill, or avowedly, like Bradley, to read into the particulars a sys- 
tem of absolute universals. 

In the next place, it is this universality of attributes that furnishes 
Mill a content for the proposition. This will appear as we examine his 
doctrine of propositions. 

Mill uses the term "proposition," rather than "judgment," because 
he regards the latter term as emphasizing too much the mental processes 
involved. It is the import, not the psychology of the judgment, in which 
he is interested, and this he thinks is best expressed in the term "propo- 
sition."' This choice of terms serves to bring into clearer setting the 
transition from an associational psychology of particulars to a logic of 
universals. For the import of a proposition is supposed to be quite inde- 
pendent of belief. It is subject to belief, but is not constituted by belief.^ 
The import is the universal meaning of what is asserted in the proposition, 
and is not conditioned by the way in which the assertion arose, or the 
service rendered by the assertion to the one making it. 

Mill does not fully face the difficulty of reconciling such 'a theory of 
propositions with his empiricism. His first analysis of the proposition 
as an assertion of something about something, upon which he dwells at 
length,^ takes its cue superficially from the verbal form, and for our 
purpose it can be passed over. Much more significant is Mill's account 
of the proposition as an assertion about facts. The true subject of the 
proposition is one or more facts.'' Indeed, matter-of-fact and assertion 
are expressly identified.^ But how can this be ? Mere particular facts 
as such are not asserted; they merely are. The assertion of a fact surely 
implies a standpoint outside the fact. How then can facts get into 
propositions ? 

'73- 

" Contrast 27c with 21J, 73a, 74a, and 756. " 121&. 

3 6'jd, and elsewhere. s 836. 



UNIVERSALITY OF ATTRIBUTES AND PROPOSITIONS 25 

Facts get into propositions by virtue of the universality of their 
attributes. Matter-of-fact and import of proposition are identical' 
because every fact can be expressed in terms of universal attributes. 
The particular existence of a fact is overflowed by its universal character, 
and it is the latter that gets recognition in Mill's proposition. Bradley's 
vigorous attack on Mill's associationism leaves this out of consideration. 
If Mill had remained a consistent associationist, Bradley's strictures 
would apply; and they are no doubt justified in so far as Mill fails 
explicitly to acknowledge a system of universals. But they ignore the 
use which Mill makes of the universal character of every fact in his 
doctrine of import. Mill rides two horses, not always very steadily 
keeping them abreast; it is not entirely clear, however, that Bradley 
does better to reduce the two to a double-natured monster, with existence 
and meaning inside one skin.^ 

The difficulties of the position, if no greater in Mill, are perhaps more 
obvious, and therefore more easily pointed out. The particular fact, 
taken as merely given, and as such independent of the knower, has to be 
matched with a universal meaning, belonging to an absolute system of 
meanings, with an import also as such independent of the knower. The 
universal character of attributes has played the trick. Committed from 
the start to particular facts. Mill finds these facts capable of description 
in terms of universal attributes, which forthwith give content for univer- 
sal propositions. Such is the transition from givenness to import, from 
fact to proposition. 

The import of propositions assumes a system of time relations, a 
system of space relations, and a system of qualitative universal attributes. 
Different attributes may evidently bear to each other time and space 
relations, and an identical attribute may appear in different times and 
spaces. These assumptions were not explicitly systematized by Mill,^ 
but they lie at the basis of the three fundamental relations of matter-of- 
fact asserted in propositions: coexistence, succession, and resemblance.'' 
To these Mill adds two other relations: existence and causation. Exist- 
ence is in the last analysis apparently reducible to the others. Causa- 
tion is a very special form of succession into whose significance we must 
inquire later, when we consider the problem it presents to inference. 

' 83b, 8sb. 

" Bradley, Principles of Logic, in various relevant passages; see especially Book II, 
Part II, chaps, ii and iii. 

3 As they have been, for example, by the neo-reaUsts. 
" 80-85. 



26 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

The whole import of propositions reduces at last to accompaniment of 
attributes.'^ 

In this view of the import of propositions Mill seems to have brushed 
aside the particulars in nature and to have grasped its universal laws. 
Nature operates always in accordance with ultimate laws that cannot 
fail to be universal. A complete statement of them would be a complete 
account of nature. Our propositions are attempts to approximate such 
a statement. "We are not sure that any of the uniformities with which 
we are yet acquainted are ultimate laws; but we know that there must 
be ultimate laws; and that every resolution of a derivative law into more 
general laws brings us nearer to them."^ The whole course of nature, 
it seems, is statable in terms of propositions, and the business of infer- 
ence is to approximate as closely as possible to such a statement. It 
matters not what prompted the statement, for the psychology of belief 
is irrelevant; the statement if correct expresses an accompaniment of 
attributes as it is in nature, entirely objective, wholly determined, and 
absolutely universal. If nature in one aspect consists solely of par- 
ticular facts, in another aspect it consists of universal laws. In his scheme 
of inductive inference Mill attempts to bring these together, though the 
result is rather to oscillate between them than to harmonize them. 

^8oc,85d. 



CHAPTER IV 
INFERENCE AS ANTICIPATION OF FACTS 

There are two ways of looking at inference. To distinguish them 
will give us a point of view from which to criticize Mill's account of infer- 
ence. On the one hand, inference may be viewed as a process, whereby 
knowledge is genuinely increased and there is an actual reconstruction 
of content. On the other hand, it may be viewed as a relation within 
content, by which one part of the content implies another. From the 
first point of view, in describing any case of inference we are bound to 
consider the state of knowledge of the person that makes the inference, 
both before and after the inference is made, and to see what has thereby 
happened to his knowledge and why it happened. Inference thus con- 
sidered is the reconstruction of a specific situation. If, in the light of 
the knowledge obtained by the inference, we then try to state by what 
right the inference was made, we pass over into the other view of infer- 
ence. The inference is then no longer a reconstruction of content, but 
a relation within content. Now the formal analysis of inference always 
ignores the process of reconstruction. It is bound to take its stand in 
the light either of the lesser knowledge preceding the inference or of the 
greater knowledge succeeding the inference; usually the latter. In 
either case the inference as a movement of thought disappears. For in 
the earlier content taken just as it stood there was no implication corre- 
sponding to the inference; that is, in the light only of the knowledge 
previous to the inference the inference cannot be seen as valid, for if it 
had then appeared as valid it would already have been made. But in the 
light of the fuller knowledge after the inference, the inference would not 
need to be made; so that when the content of the later knowledge is 
analyzed to find an inferential relation within it the inference appears 
to be tautologous. Taking inference then as a relation within a fixed 
content, it must be either invalid or tautologous; the premises either 
involve the conclusion or do not.^ In the study of inference there is of 
dourse a place for formal analysis; it need not mislead if, while we pro- 
visionally take that point of view, we expect the inference as analyzed 

' "If the Syllogism yields novelty, it begs the question. If it disclaims novelty, 
it becomes vain repetition. As a form, therefore, it is either futile or false" (Schiller, 
Formal Logic, 208). This applies to all formal proof. 

27 



28 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

to appear either tautologous or invalid. We can at once escape this 
dilemma by returning to the other point of view, from which we con- 
sider the inference as it was actually carried through. To do this with 
full consciousness of what it means would reconstruct the formal analysis 
of inference, and would relegate it to a subordinate place. 

It is to the credit of Mill that in his theory of inference and its rela- 
tion to fact he set out to introduce a logical reform of this kind. He 
proposed a logic of truth instead of a logic of consistency.' He made 
inference pass from the known to the unknown, a process of discovery. 
It was to proceed from particular facts, and to lead to particular facts. 
Mill certainly was feeling for the concrete process of inferential recon- 
struction. Yet in detail he failed to maintain this attitude. His con- 
ception of facts as definitely given interposed itself, and prevented him 
from appreciating the concrete and really significant reconstructive 
function of inference, so that he fell back into the formal attitude toward 
inference as a relation of content. Endeavoring then to extricate him- 
self from this formal position, and to recover the reconstructive process 
of inference which he had lost, he comes upon the experience of actual 
discovery, but regards it for the most part as only subsidiary to inference, 
and even to the end fails to grasp its real function in inference and its 
true relation to fact. 

In this way Mill oscillates between three quite different conceptions 
of inference. The conception with which he sets out is that of antici- 
pation of experience. On the ground of given facts other facts are 
anticipated. His formula for such inference is "from particulars to 
particulars." The establishing of this as the character of inference Mill 
believes to be a vindication of empiricism.^ A universal need not inter- 
vene between the particular facts on which the inference is grounded and 
the particular facts to which the inference points; if a universal does 
intervene it is accidental, merely a convenient safeguard against error. 
Nevertheless it appears that a universal always could be made to inter- 
vene, and if an inference is justified at all, then by the same token a 
universal is justified. Thus Mill comes to the second conception of 
inference as the proof of universal propositions. The main body of his 
inductive technique is built on this conception. But inference as the 
proof of propositions cannot finally leave out of account the source of 
propositions, the way in which they come to be proposed for proof. 
Inference, in short, is variously considered by Mill as the anticipation 

' 2s, 236c. 

' Liard, Les Logiciens Anglais Contemporains, sth ed., 24-27. 



INFERENCE AS ANTICIPATION OF FACTS 29 

of particular facts, the proof of universal propositions, and the discovery 
of universal propositions, though Mill seems unaware that he has shifted 
his ground in passing from one to the other. Mill is not at fault, indeed, 
in holding to these three conceptions as genuine aspects of the inferential 
process ; his error is in treating each in isolation from the others and in 
misconceiving the relation of each to facts. Let us examine each of the 
three in turn. 

Mill finds inference generally acknowledged to be of two kinds: 
inference from particulars to generals, and from generals to particulars, 
or induction and ratiocination, the latter being expressed in the syllo- 
gism.' Mill upholds a third type of inference, not only as valid, but as 
" the foundation of both the others." Indeed "all inference is from par- 
ticulars to particulars."^ A universal may or may not intervene; if it 
does, it merely breaks up the inference from particulars to particulars 
into two parts, the first ending with the universal, the second beginning 
with it. The actual inference is always from particular facts to other 
particular facts, and whether it passes through the universal on the way 
or leaps directly from facts to facts without a universal does not alter 
the nature of inference as such. The general proposition is merely a 
register of inferences already made from the facts, or a formula for 
making more. 

The doctrine then is this, that inference is in its nature a passage 
from particular facts to other particular facts^ without the necessary 
mediation of a universal. There are several fundamental difi&culties in 
this conception of inference. 

First, there is such a process in experience, but it is unreflective, and 
cannot properly be called inference. It is habit. When Mill offers 
examples of inference which shall be purely from particulars to par- 
ticulars, he finds himself reduced precisely to cases of habit.'' The 
avoidance of fire by the child, and by the dog as well, and the skilful use 
of weapons and tools — these do involve anticipations of experience on 
the basis of previous experience, but they are not logical processes. In 
some cases they may have grown out of an earlier inferential process, but 
they need not have done so. They may rest on purely unreflective asso- 
ciation. The mother who prescribes a remedy to a neighbor's child 
because it cured her own Lucy^ can scarcely be supposed not to make 
some use of a " general proposition " ; but if she does not, as Mill assumes, 

' 125c. 

' 146c. '' 142^, 143a, c, 144a, b. 

s Or to one other. s 1436. 



30 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

then she has made no inference at all, but repeats an operation under 
repeated circumstances by mere force of habit. 

Secondly, when action rises above mere habit and becomes reflective, 
a universal is required. A particular, if reflectively taken as a particular, 
implies a universal. Mill begs the question when he finds himself bound 
to call the particular facts "cases."' An inference from facts to facts is 
justified only if both sets of facts are seen to be cases; cases, that is, to 
which the same rule will apply; cases of the same universal.^ 

The emphasis on the universal, it is true, may be shifted either to the 
beginning of the inference or to the end The universal may then be 
alternately located at either end of the process. If the cases /rom which 
one infers are considered as particular, then any case to which one infers 
is only one of an indefinite number of possible cases, or is the application 
of a law. If the cases to which one infers are considered as particular, 
then they are anticipated on the basis of the law which was exemplified 
in the cases from which one infers. That is, one infers either from par- 
ticulars to a law which includes other particulars or to particulars from 
a law that is exemplified in previous particulars. One may be more 
concerned under given conditions with the origin or with the application 
of the law, but cannot dispense with it as essential to the inference. 
Mill seems to do so only because he oscillates from one end of the process 
to the other, in each case leaving the universal to operate at the opposite 
end. In the one case the general proposition is a register of observations, 
and the inference is still to take place ;3 in the other case the inference 
has already taken place, and the general proposition is a formula for 
making more inferences like it.'' Between the two the inference plays 
successful hide-and-seek with the universal. 

That inference cannot dispense with a universal is due to the h)^©- 
thetical character of the latter. The universal cannot itself be experi- 
enced, and is never a mere record of past experience. It represents a 
hypothetical interpretation of any future experience so far as it can be 
taken in terms of the past experience.^ Past experience points to like 
future experience if it is really the same. If the unobserved particular 
is a similar "case," the inference is valid. The transition through the 
"if" signifies the mediation of a universal. 

' 1256, i4id, 1490. 

2 "A general truth is but an aggregate of particular truths; a comprehensive 
expression, by which an indefinite number of individual facts are affirmed and denied 
at once" (i^id). But "aggregate" and "indefinite" are contradictory, and this 
contradiction lurks ever}rwhere in MiU's treatment of "cases." 

3 141C, 147&, 1516. '' 142a, b, i486. 5 isoe. 



INFERENCE AS ANTICIPATION OF FACTS 31 

What do we mean by the universal in inference, and why is it needed ? 
It is true that all problems and all solutions and therefore all inferences 
are specific. Had Mill, by the use of his formula "from particulars to 
particulars" intended to support this aspect of inference, he might well 
have pressed it farther than he did. But he omitted the reflective ele- 
ment of inference, the necessity we are under to carry with us a set of 
possible interpretations of new experience. This interpretative tendency 
is the universal; it is what renders inference reflective where habit would 
be unreflective. In actual use the universal has no absolute meaning. 
Absolute meanings are fictions of the logician. When we interpret what 
we take to be the new "cases" in "the light of" the old, that light is the 
universal.' It is the deliberate readiness to treat them, when under the 
pressure of uncertainty, as cases. General language has crystalhzed 
these interpretations into a highly elaborate system, with its own tech- 
nique; but the relative independence and permanence of the language 
must not be allowed to obscure the essentially instrumental character 
of the universal which the language expresses. It is here that Mill failed 
to free himself from the conceptions of formal logic, and let go the very 
factor which would have revitalized his system: the play of the universal 
as the reflective interpretation of new experience in the light of the old. 

Thirdly, Mill's attack upon the syllogism as a petitio principii is due 
to this failure to appreciate the interpretative function of the universal 
in the actual process of inference. All inference, if treated as he treated 
the syllogism, becomes a petitio; for the syllogism avowedly expresses 
the content of the inference after it has been made, and is therefore 
tautologous. All inference, when passed through and looked back upon, 
must appear tautologous; if its content did not admit of tautologous 
statement it would be invalid. Mill's strictures apply equally well to his 
own inferences from and to particulars. Are the earlier and later facts 
both "cases" ? If they are not, the inference is not valid. If they are, 
then no inference is needed; for the later cases merely add themselves 
to the earlier as more of the same. Just so long as Mill takes the content 
of his particular facts in the same fixed and unquestioned way in which 
he takes the premises of the syllogism, all actual inference is inevitably 
shut out. 

' Through the collision and breakdown of habits their content becomes reflective. 
This reflective content of what was a habit is now a universal. We continue to gain 
universals in this way; but after this type of experience is once estabUshed the system 
of universals may be built up in other ways, as by verbal instruction. The materials 
of the universal must always have arisen out of what was unreflective. 



32 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

Fourthly, this suggests the difficulty that in Mill's scheme of inference 
the fundamental function of inference in meeting an attitude of inquiry 
is ignored.' Mill takes the knowledge of certain facts and proposes to 
infer other facts from them. If this is merely the addition of more facts 
it is not inference, as we have seen. It is inference only if the facts are 
not adequately known. In any actual case of inference the primary 
problem is to ascertain what are the facts. We should have no occasion 
to think of facts in a situation that — so to speak — was all fact. A 
"question of fact" emerges because the situation contains more than 
mere fact; it contains (i) certain contradictions or difficulties that impel 
to further inquiry about facts; (2) various more or less tentative con- 
structions which aim to clear away these difficulties. 

Here we strike the root of the matter. Mill has a favorite formula 
for inference which describes it as procedure from the known to the 
unknown.^ This formula may no doubt be given an interpretation which 
renders it a correct description; but it is quite as correct to say that 
inference is procedure from the unknown to the known. When facts 
are adequately known there is no occasion for inference. But when our 
knowledge of the facts breaks down, and it is not known just what the 
facts are, then inference comes in as an effort to interpret the facts in 
such a way that they shall be adequately known. Inference, one might 
say, aims to transform the unknown into the known. The relation 
between inference and facts is never so simple or so one-sided as Mill 
supposes; it is a relation of mutual dependence. 

In view of this attitude of inquiry that underlies all inference it is 
necessary to reject in principle the sharp distinction Mill maintains 
between the earlier cases which justify the inference and any later case 
to which it is applied, though in the practical technique of inference the 
distinction has a relative value. The facts which prompt the inference 
are first determined as "cases" by the inference, which is designed to 
meet one of the two questions: "Of what are they cases?" or, "Are they 
really cases ?" They are therefore the very facts to which the inference 
applies. It is true of course that an inferential situation may be ex- 
tremely complex, some factors in it more fixed, others more fluid; and 
at successive stages of the process it may be useful to consider some the 
data and others the conclusion. Yet in principle Mill's sharp separation 
of the data and the conclusion must be denied. In inference we do not 

' This consideration has been well worked out by Professor A. W. Moore, of 
Chicago, in a seminar on "Modern Logical Theories," to which the writer is greatly 
indebted. 

" 1256, 126a, 139a, 2ioe, 223(^-240. 



INFERENCE AS ANTICIPATION OF FACTS 33 

first get a set of facts, ticketed and fully known, to serve as data of an 
inference, and after an interval another fact conveniently ticketed to 
receive the application of the inference. That, as we have seen, would 
be a fair description of the operation of habit, if under knowledge of any- 
thing we were to include any ability to deal with it. But it is not a 
correct description of inference. In inference the data and the con- 
clusion must come together in organic relation, and it is precisely at the 
point where they do come together in a single interpretation that infer- 
ence takes place. 

In short, Mill's account of inference from particulars to particulars, 
which actually applies better to habit, implies two situations, an earlier 
and a later. He oscillates between these, because he seems vaguely to 
have perceived that in either of them inference may appear. There is 
no inference unless some factor in the situation is brought into question, 
but the question may turn upon the formulation of a new universal or 
upon the selection of an old universal. In both formulation and selec- 
tion of a universal the "cases" are seen to be such only in relation to the 
universal, but in the one the question looks toward the universal, in the 
other it looks from it. This is to say that either the major or the minor 
premise of a possible syllogism may be placed in question. Mill is 
right in breaking inference from particulars to particulars into two parts; 
but wrong in considering the universal an unessential division-point 
between them. He is right in excluding inference sometimes from one 
part and sometimes from the other; but wrong in denying that it may 
be in either. 

Indeed, Mill's position is shifted when he comes to consider the tech- 
nique of inference. He virtually recognizes the necessity of the universal 
when he acknowledges that any data which justify an inference to a 
particular will justify an inference to a universal as well,^ and that the 
validity of the inference can be shown only by drawing the universal 
explicitly.^ Thenceforth in his discussion the process of inference is 
made to consist in the establishing of general propositions. He might 
well have explicitly taken the same step with reference to the second half 
of his original type of inference, in the selection of a universal to explain 
a given situation. He admits this to be often a most arduous intellectual 
process, but refuses — though not always consistently — to grant it the 
status of inference,^ on the ground that it is invention, and "invention 
cannot be reduced to rule." These two phases of inference remain to 
be considered in the next two sections. 

' I48c-49ff, 155c, 208a. ^ 154^-556. 5 208-9. 



CHAPTER V 
INFERENCE AS PROOF OF PROPOSITIONS 

The distinction just noted between the estabUshment and the selec- 
tion of a universal proposition enables Mill to pass over to a second con- 
ception of inference. Before examining the latter it will be well to note 
again the exact point of the transition. Mill has established, he believes, 
the general character of inference as a passage from certain particular 
facts to certain others. But if these certain facts justify the conclusion 
about any others at all, they justify the conclusion about any others 
whatever of the same description. Accordingly from premises which 
justify any conclusion we can always draw a general conclusion. The 
problem of application, the problem, namely, whether the later facts are 
of the same description, or of what description they are, is thrown out 
as irrelevant to inference, because it cannot be reduced to rule; it is 
apparently too psychological. This leaves for inference only the prob- 
lem of drawing the general proposition from the data, the problem of 
induction. 

But this is not all. There is a still further limitation in this concep- 
tion of inference as induction. It is not the discovery of general propo- 
sitions but their proof with which he concerns himself. The type of 
question which his machinery of induction is designed to solve is not, 
"What proposition is true ? " but rather, "Is a given proposition true ? " 
Mill set out, it is true, with the intention of providing a logic of discovery,^ 
of the process of advancing from known truths to unknown.^ Logic is 
to investigate the "pursuit of truth, "^ of "how we come by that portion 
of our knowledge (much the greater portion) which is not intuitive. "^ 
But he makes this synonymous with "estimation of evidence, "^ and falls 
back at once into a formal logic of proof. ^ "Our object," he says, "will 
be .... to ... . frame a set of rules or canons for testing the suffi- 
ciency of any given evidence to prove any given proposition. "^ 

Why did Mill's conception of inference become so completely that of 
proof ? There were probably two reasons, both suggested in the words, 
just quoted. The first is extrinsic to the character of his theory, and is 
due to his desire to provide, in a logic of induction, a set of "rules and 

' 2o8a. 3 ig6. 5 23&. 

^236. ■• 276, sia. * i2ia, 216, 45a, 88&, 208^. '23c. 

34 



INFERENCE AS PROOF OF PROPOSITIONS 35 

canons" that would emulate those of the formal deductive logic in which 
his father had given him so rigid a training; Mill certainly took great 
satisfaction in the formulation of his "inductive methods."^ The other 
reason is intrinsic to the theory itself, which drove him back to "given 
evidence" for "given propositions." Facts for Mill are always given, 
whether subjective facts of immediate consciousness or objective facts 
of the system of nature. The proposition is likewise given, for it is the 
universal meaning of the facts, to be read off from them as they come 
together. 

The universal propositions the inductive proof of which constitutes 
inference are of various kinds. They include the statement, for example, 
of spatial and numerical relations.^ It would be interesting to trace 
out the relation of inference to matter-of-fact in these, and to inquire 
whether it is consistent with Mill's general treatment of induction. That 
treatment, however, is based almost entirely on the establishment of 
causal relations,^ and the present criticism of Mill must be limited to this 
field. 

The character of induction as proof is rooted in Mill's realistic scheme 
of nature, (i) Nature consists, as we saw, of certain things, having 
certain attributes and in certain collocations. (2) Every change takes 
place according to a uniform law of succession, each event following and 
preceding certain other events according to such a causal law. (3) Nature 
is a single system of such things and events. This whole system of nature 
is conceived as definitely determined and proceeding on its way inde- 
pendently of us.'' To be sure, we are not acquainted with all of it, but 
we are certain that it is all of this character. When we wish to know 
what the laws of sequence in nature are we must watch the shuffle of 
facts and observe which go together. Our experiments may vary the 
shuffle, but the principle of noting the shuffle is the same. The very 
possibility of identifying the facts in the shuffle rests upon the universal 
character of their attributes, and the assertion of the accompaniment of 
certain attributes is a general proposition. It would seem, then, that 
discovery and proof are essentially identical. We find accompaniment 
of attributes so far as, within the field of our observation, there is accom- 
paniment of attributes. The facts that teach us the law prove the law. 

' Mill hoped that his Logic might serve as a Novum Organum of real practical 
value. See Logic, 579-80; Autobiography, 226. Cf. Joseph, Introduction to Logic, 342 . 
^234i. 

3 23s6-(f, 236c. 
* These are the "three analogies" in Mill, as noted above. 



36 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

This would seem to be a fair statement of the general conception 
of proof which underlies Mill's theory of induction. But the matter is 
not so simple as it seems. There are grave difficulties raised by it. 
Partially recognized by Mill, they compel him to introduce deviations 
in the procedure of induction. Fully faced, they would lead to a recon- 
struction of its underlying principles. Three such difficulties require 
our consideration: 

First, the inductive methods are all recognized by Mill to be so many 
means of elimination.^ But elimination is not proof; it is disproof. 
Elimination must obviously operate upon alternatives; and the very 
point of the elimination is that neither of the alternatives is proved till 
at least one other is disproved. There must be a tentative consideration 
of various apparent uniformities in order that the methods shall have 
play in the rejection of those which are actually non-uniformities.^ 

Mill might be supposed to answer that this is just what nature does 
for us. Out of the chaos of sequences, some accidental and some uni- 
form, the accidental are eliminated by the circumstance that they do 
not recur, which is the principle of the methods, ignoring for convenience 
their finer complications. But there is no elimination whatever in nature. 
The facts are all there, and they stay there. Nature is wholly careless 
whether she presents uniformities or non-uniformities. It is the reflect- 
ive attack upon nature that uses the methods, and their eliminative 
procedure is exercised upon the tentative efforts to interpret the facts; 
that is, to find out what the facts really are. Mill's proofs are disproofs: 
disproofs of propositions not given ready-made by the facts that furnish 
the disproofs. 

Where, then, do the propositions come from? Whence arise the 
assertions about the facts, the interpretations of fact, which are then 
proved or disproved? To ask such a question, it must be replied, is 
very likely to imply just Mill's misconception. We have no system of 
facts, complete and ready-made, with which to check up our interpreta- 
tions for elimination. There is a constant interplay between fact and 
interpretation, each reconstituting the other. The only facts we have 
are the facts as we have successfully interpreted them, and our interpre- 
tations always arise as tentative statements of the facts. Again, the 
operation of proof and disproof is strictly correlative with the presenta- 
tion of propositions to be tested out; neither can be supposed without at 
least a tentative form of the other. Nature no more offers a series of 

' 278^, 279e-8oa, 281a, 310&. 

^ I.e., which are not unconditionally invariable. 



INFERENCE AS PROOF OF PROPOSITIONS 37 

prepared "evidences" ready to apply to any given proposition tlian she 
provides the propositions ready-made. Facts are not all in nature, 
inferences all in us. Facts likewise grow in the soil of inquiry, and are 
the fruits quite as much as the roots of our inferential control of nature. 
The second difficulty is due to the impossibility of determining the 
limits of a fact out of relation to the character of the inquiry about the 
fact and the proposed interpretation of the fact. It is the difficulty, in 
any inquiry regarding cause and effect, of setting the limits of an 
event." Mill is already feeling this difficulty when he draws his distinc- 
tion between causation as practically and philosophically understood.^ 
Causation, according to his own program, is to be understood in the latter 
way; that, he holds, is the conception underlying genuinely scientific 
inference, and is based on the facts of nature as they really are. For 
practical purposes, indeed, we are content to note a selection of the 
conditions of an event and to call them the cause, or to take two events 
whose succession is more or less mediate and call them cause and effect, 
without taking account of all the possible counteracting conditions that 
might have intervened. But in philosophical strictness we should do 
neither the one thing nor the other. Philosophically, causation must 
admit no omissions and no loopholes.^ Now, having set this up as a 
demand, what Mill actually does in various illustrations is to contrast 
more nearly philosophical with less nearly philosophical statements of 
concrete cases of causation, but all his illustrations are statements of 
approximation only; they never exhibit a single case of causation in 
the full "philosophical" sense. And they do not because they cannot. 

' The best discussion of this difficulty seen by the writer, though without special 
reference to Mill, is in Sidgwick, The Process of Argument, chaps, x and xi. A few 
sentences must be quoted. " The question where does an occurrence end and ' another ' 
begin is unanswerable except by an artificial distinction drawn to suit our practical pur- 
poses." "This kind of analysis may be carried much farther. Given any two steps 
in the series, we know that some occurrence comes between them, however short the 
interval, and that this intermediate occurrence .... has just as much right to be 
classed as belonging to one end of the chain as to the other. It is not properly a chain, 
in fact, but a stream, or a continuous growth like that between bud and flower." 
"No one seriously denies that the links are there, but our practical needs do not always 
compel us to explore them." "The separation into Cause and Effect is done for a 
purpose, and its value depends on its serving that purpose. Whenever a hitch occurs 
we are bound to look more closely into the details of the connection." "The Une we 
draw between antecedent and consequent is an artificial one; they are more or less 
ill-defined parts of a whole which it suits us to pull asunder." 

^ 240c, 2410. 

3 Logic, Book III, chapter v as a whole. 



38 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

For if Mill were to be pressed on the point, he would find himself 
completely locked in by the Kantian antinomies. The continuity of 
time and space renders all change continuous, and there is nothing in 
the facts taken as they merely "are" — assuming they could be so taken 
— that would ever indicate the limits of an event, either serially or in 
section. The continuity of all process in space and time, and perhaps 
also in qualitative degree, renders the singling out of any "event" pos- 
sible only when relevant to a purpose. Mill admits this for "practical" 
causation, but he has to assume it covertly for all causation.' 

The point may be restated thus: Mill reduces the uniformity of the 
world to a network of particular uniformities of sequence between a 
group of antecedent phenomena and one consequent phenomenon. This 
is a correction of the common, crude view (in terms of which, however, 
Mill often speaks) that every consequent is the result of some one ante- 
cedent, each phenomenon being taken as though an obviously definite 
unit. But the parts of the world and their properties are more closely 
intertwined than we crudely suppose. So Mill corrects this view in two 
respects: First, he insists that in the cause we should enumerate all the 
conditioning antecedents; that is, all the antecedents whose combina- 
tion is required that the effect may follow. All the conditions, positive 
and negative, are absorbed into the cause. Secondly, he insists upon 
the immediate succession of antecedents and consequent. There must 
be no intermediate steps between. The reason of this is that there may 
be unsuspected conditioning factors, and with the longer interval and 
the more opportunity we give unsuspected factors to operate the more 
likely it is that the expected sequence will not hold. A plot which is to 
culminate in a year is more liable to be frustrated than one which is to 
culminate in a day. Mill, it is true, does not correct the popular idea 
of effect as he does that of cause. He still selects some one consequent 
which he calls the effect, and thus gives room for the plurality of causes.^ 
Theoretically this is an inconsistency. An effect is just as complex as a 
cause, and if we enumerated all its elements the plurality of causes would 
be impossible. Practically, of course. Mill is quite right; there would 

' The supposition of "points" and "instants" is a mathematical refinement 
intended to provide a union of continuity and discreteness by bringing space and 
time into correspondence with the filled number system. But when we try to apply 
the formulae based on this supposition, the question of what points and instants to 
start with raises exactly Mill's "practical" problem over again, and cannot be met 
out of relation to a purpose which is dealing with the system of points and instants. 

^ See an acute discussion of plurality of causes in Hobhouse, Theory of Knowledge, 
457-62. 



INFERENCE AS PROOF OF PROPOSITIONS 39 

usually be no gain in looking for all the elements in the effect. We are 
not usually so interested in the reasons of things as in how to bring about 
a particular result. But philosophically speaking, as Mill would say, 
we have a right to hold him to just as wide an extension of the effect as 
of the cause. Now whfen we try to make this view of causal sequence 
theoretically correct, how are we to decide which of the antecedents and 
consequents are relevant and which are not ? A finite mind can never 
grasp all the antecedents. Unsuspected factors constantly enter, and 
may at any time prove important. Those which we commonly reject 
because too trivial or remote have an influence upon the effect which 
though at first perhaps infinitesimal may in time become vast. Theo- 
retically, therefore, we should enumerate all the antecedents and conse- 
quents in the universe. Could we do this, we might say with confidence 
that were this cause ever repeated its effect would be repeated, and this 
without reference to the immediateness or remoteness of the cause and 
effect. This is the uniformity of sequence carried in one direction to its 
theoretic limit. Within this limit there must be uncertainty and imper- 
fection in our grasp of causal laws. But this limit if theoretically perfect 
is obviously useless. Again, uniformity of sequence might be carried 
to theoretic perfection in another way. If the antecedents, as we have 
seen, are perfectly known, the certainty of the sequence will be absolute, 
no matter how great the interval between antecedents and consequents ; 
there need be no time limit. The reverse is true, that if the antecedents 
are not completely known the probability of the sequence is less as the 
interval between the antecedents and consequents is greater. If, how- 
ever, we bring them into relatively close proximity the probability of 
sequence becomes relatively great. The limit is reached when the time 
interval has become infinitesimal. We have then a mere tendency in the 
antecedents which awaits no interval in which it might be interfered 
with, and is therefore perfectly certain however small we make the group 
of antecedents, down to the infinitesimal limit. This result, again, is 
theoretically perfect but practically useless. Mill is locked up within 
the dilemma of a construction of causation which is either theoretically 
incorrect or practically of no avail. ^ 

Indeed, this is an underestimate of the difficulty. We cannot call 
the limiting forms of the causal scheme even theoretically correct; they 
are entirely meaningless. It must be remembered that the problem of 
causation is to find uniform sequences, and it will be no solution simply 

' Venn, Empirical Logic, 47-72, gives an excellent analysis of the antinomy of 
causation in Mill. 



40 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

to eliminate the problem. If now the absolute certainty of a sequence 
is assured by screwing the antecedent and consequent so close together 
that no interval is left in which the sequence might be counteracted, the 
time relation has disappeared, and this destroys the sequence itself whose 
certainty it was sought to safeguard. If in the other direction the whole 
universe is included in cause and effect, the time limit spreads out to 
infinity, the history of the universe becomes a single event, and sequence 
is once more destroyed. Theoretically considered, then. Mill's view of 
nature as a set of given facts in causal relation breaks up into antinomies 
when pressed in either direction. We are compelled to return, as Mill 
did in his actual examples, from the philosophical to the practical view 
of causation. But to do so requires that we have a criterion of what 
shall be taken as a single fact, and such a criterion is not provided in the 
facts themselves in their mere given aspect. In causation practically 
considered such a criterion is provided; it is found in the personal rela- 
tion of the inquirer to the situation. As this criterion is relative to the 
inquirer. Mill rejected it as practical, and the conception of causation 
in which it operates as unscientific. But the conception of causation 
which aims to be free from this defect collapses for lack of such a 
criterion. Once more it is seen that there is no place for inference in a 
world of pure fact. 

This suggests the third difi&culty, that proof, as proof, turns out to 
be merely a relation within given content, as was pointed out above. 
It is no longer a means of passing from one state of knowledge to another, 
such a function appearing irrelevant to its character as "given evidence" 
of a "given proposition," but it is now a relation within the content of 
a single state of knowledge. We have already seen how any inference, 
viewed ex post facto, must be as circular as the syllogism. This circularity 
centers in the very nature of mere proof, its evidential character lying as 
a fixed relation within its own content.^ 

How tautologous, for example, are Mill's proofs of causal laws. He 
takes his instances, already selected as relevant, orders them under the 
formulae of the methods, and points to them for the proof. It is there, 
in them, as they stand. The evidential relation lies within a content 
assumed to be already completely determined. 

' "While the process of thought is still active, the logician .... has nothing to 
say to it; for his vulturine 'analysis' never ventures to attack a living thought. He 
appears upon the scene when the thinking is defunct and over 'Logical analy- 
sis' first destroys the real connections between thoughts, and ihea feigns false ones" 
(Schiller, Formal Logic, 197-98). 



INFERENCE AS PROOF OF PROPOSITIONS 41 

Proof in this static sense resembles a map by which one may and 
often does represent the journey one has pursued. In the map, as in 
the proof, the actual movement or passage of the journey is lost, and 
that which was discovered in the course of the journey is represented 
simultaneously with the starting-point. Experience cannot be repro- 
duced in a formula. It can be represented, but the adequacy of such 
representation is always relative to its purpose. Moreover, in the proof 
as on the map one may indicate a route that has never been actually 
followed. One may even amuse one's self by constructing endless maps 
and proofs without having journeyed or reasoned at all. And just as 
the route when projected on the map lets slip the real story of the 
journey, so proof fails to embody the actual process of inference, the 
account of which in the end must necessarily be given as a part of some 
one's personal biography.^ The results of a scientific discovery are 
ordinarily our sole concern; having set them out in systematic relations 
with our other knowledge, we call this their evidence. But if we do 
undertake to give an account of how the discovery was made, we are 
drawn back to its setting in the life-story of the scientist. Our systema- 
tized "proof" of the discovery does not reproduce either the problem or 
the solution as these originally appeared to the discoverer. Inference 
as discovery will be further considered below. 

It may be worth while to illustrate this point in a different field. 
Consider the case of a debater, whose mind is definitely made up on the 
main question, but searching for arguments with which to convince his 
hearers. This man certainly has a problem before his mind, but it is 
not the problem expressed by the question in debate. It is the problem 
of selection of materials that shall stand in certain relations to other 
materials. This relation may, if you please, be called evidential. It is 
intended to operate in an inferential process in the hearer's mind. But 
to the debater's own mind^ that so-called evidential relation does not 
operate inferentially, and the selection of evidential materials is no more 
inference for him, as regards the question in debate, than would be the 
selection of rhyming words or the parts of a puzzle picture. Proof, then, 
may mean two different things. It may mean either the reconstruction 
of content by which an actual inquiry is met, or a relation within the 

' In the last analysis is not the historical more fundamental than the scientific 
point of view? This is perhaps the ultimate issue between instrumentalism and 
intellectuahsm. 

2 And to the hearer's mind when the debate is over and he reviews the argument 
as a whole. 



42 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

content as it is looked back on by the inquirer after the reconstruction, 
or as it is supposed to apply to the problem of some other inquirer. 
Under the first alternative proof is evidentially operative in an actual 
inference; under the second alternative it is not. The latter is "formal" 
proof. 

Proof in the latter sense may reach any degree of detachment from 
actual inference. The content, and the so-called inferential relations 
within it, may become indefinitely abstract and schematic. Such is the 
case, for example, in the field of mathematics and of mathematical logic. 
The inquirer indeed does form a succession of inferences about the con- 
tent as he is building it up, but the relations of "implication" exhibited 
in the content after it is built up are not inferences at all in the same sense; 
or perhaps in any proper sense.^ 

As the difficulty presents itself in Mill, it seems that the facts must 
already have been determined before proof appears, and the proof is of 
the nature of an ex post facto reading of the facts after the real inference 
has been made. This view of proof leaves untouched the question of 
how the facts were determined. This question receives partial considera- 
tion under Mill's treatment of hypothesis, to which we now turn. 

' In criticizing this sentence of Adamson, "No logical method can be developed 
save from a most definite conception of the essential nature and modus operandi of 
thinking," Professor Marvin says, "To which the reply can in the present day be given: 
'But it has been done, such a symbolic logic actually obtains'" {Journal of Phil., etc., 
May 8, 1913, p. 275). Even in the present day the claim of symbolic logic to be 
independent of the nature and method of thinking might be challenged. Its whole 
scheme of implicational relations is only one stage in the development of an instru- 
ment for the use of actual thinking. 



CHAPTER VI 

INFERENCE AS DISCOVERY 

In his formulation of the inductive methods, Mill set out to describe 
the process by which general propositions are established. As the induc- 
tive methods are merely means of elimination among alternative propo- 
sitions, the outcome is to reduce inference to disproof. But Mill cannot 
permanently lay aside as merely psychological the question of how we 
get the alternative propositions upon which disproof is to operate. He 
is forced to acknowledge a place in inference for the formation of hypoth- 
eses. Inference as discovery inevitably involves a hypothetical approach 
to the conclusion; and this may fairly be called Mill's third conception 
of inference. In answer to the question where we get the propositions 
to be established, we must say that they come as hypotheses. 

The official place of hypothesis in Mill's doctrine of inference is two- 
fold.^ First, it appears as a means of extending the "method of deduc- 
tion," by substituting a supposed proposition where no suitable one is 
known, and testing it by the consequences drawn from it.^ Secondly, it 
appears in several of the processes subsidiary to induction, processes that 
have to be performed before induction is ready to operate. At neither 
point is the process of forming hypotheses given a central, constitutive 
part in inference. Mill can still speak of "perfect induction without any 
mixture of hypothesis, "^ or of a " theory " that has in it "nothing, strictly 
speaking, hypothetical."'' 

At one point or another of his discussion, indeed. Mill is obliged to 
acknowledge a hypothetical factor at every step of inference. These 
admissions appear mainly in the sections that deal with "subsidiary" 
operations, and the most significant of them appear in passages added, 
under stress of controversy, in the later editions of his work. They do 
not lead Mill to reconstruct the non-hypothetical character of his view 
of inference and its relation to fact. But they do allow a tentative 
factor through the whole process of inference as it is in operation. Con- 
sider, for example, his treatment of analogy .^ Analogy is recognized as 
hypothetical; but all inference is analogical in so far as it is a taking of 

' On Mill's doctrine of hypothesis see Dewey, Studies in Logical Theory, 160-68. 
^ 350&, c. ■• 3606. 

3 3596. s Book III, chap. xx. 

43 



44 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

one situation to be like another. Again, abstraction or "the formation 
of concepts"' is but another name of hypothesis. Mill shows with 
admirable clearness that the mere naming of a fact implies that one has 
already interpreted it in terms of other experiences, though apparently 
he had not thought of this when he based inductive proof on "cases." 
"We cannot describe a fact without implying more than the fact." "An 
observation cannot be spoken of in language at all without declaring 
more than that one observation; without assimilating it to other phe- 
nomena already observed and classified."^ Mill gives some striking 
descriptions of the method by which one meets actual problems, as in 
"the search for a lost object,"^ or the unraveling of "the true history of 
, any occurrence from the involved statements of one or of many wit- 
nesses." "He extemporizes, from a few of the particulars, a first rude 
theory of the mode in which the facts took place, and then looks at the 
other statements one by one, to try whether they can be reconciled with 
that provisional theory, or what alterations or additions it requires to 
make it square with them. In this way .... we arrive, by means 
of hypotheses, at conclusions not hypothetical."'' 

Of special interest are Mill's admissions that any experiment — and 
the inductive methods are all essentially formulae of experimentation — 
receives its very point from the hypothesis it is to test. "All experi- 
mental inquiry assumes provisionally some theory or hypothesis, which 
is to be finally held true or not, according as the experiments decide." 

"The theory itself preceded the proof of its truth It had to be 

conceived before it could be proved All the true theories in the 

sciences .... began by being assumed."^ "Nearly everything which 
is now theory was once hypothesis. Even in purely experimental science 
some inducement is necessary for trying one experiment rather than 
another."^ This conflicts with the statement assigning the place of 
hypotheses in Mill's original scheme, that they "are invented to enable 
the Deductive Method to be applied earlier to phenomena";' for it is 
only on the prompting of hypotheses that the deductive or any other 
method is ever applied at all. Without hypothesis Mill's own methods 
would be open to the strictures he brings against Bacon's step-by-step 
method.^ His attempt to work out a set of inductive methods as self- 
contained and non-tentative in their "proof" as the syllogism had 
seemed to be has broken down. 

' Book IV, chap. ii. ' 45 2a, b. ^ 4636. 

4 354. The final words, "conclusions not hypothetical," could be accepted only 
subject to the interpretation given below, that they differ only in degree and function. 
s 1846-850. ' 353c. ' 350b. * 603C-046 and note. 



INFERENCE AS DISCOVERY 45 

But however wide a scope Mill is finally compelled to grant to the 
operation of hypothesis, he does not adequately appreciate the organic 
interrelation of hypothesis and fact. Indeed, he allows hypothesis too 
much scope. "An hypothesis being a mere supposition, there are no 
other limits to hypothesis than those of the human imagination; we 
may, if we please, imagine, by way of accounting for an effect, some 
cause of a kind utterly unknown, and acting according to a law altogether 
fictitious."^ This extreme statement, it is true, receives some limita- 
tion later on; but without sufficiently clear recognition of the principle 
that every genuine hypothesis makes a tentative claim to be fact. Mere play 
of the imagination may have aesthetic or other values; but only as a 
hjrpothesis is a genuine and controlled effort to grasp the facts, and 
because it is that, does it hold any place as a tentative inference. There 
is an organic interrelation between hypothesis and fact. In actual 
inference the two are not held over against each other. Hypotheses are 
simply our best grasp of the facts — tentative, but genuinely objective— 
at any one stage of the proceeding. Facts are hypotheses that no longer 
require a tentative attitude, but have obtained acceptance. Between 
the two there is progressive interaction, and this interaction constitutes 
inference. 

Hypotheses, according to Mill, are of two kinds,^ in one of which the 
existence of the cause is acknowledged but its law of operation is sup- 
posed; in the other the law is acknowledged and the cause supposed. 
Of this second kind there are again two varieties : the hypothetical cause 
may be a supposed collocation of agents of a known kind^ or a supposed 
agent of an unknown kind. The last variety, however, must either be 
the supposition of a law, in the form of certain properties of the agent, 
and so fall under the first head, or it collapses into a merely verbal form, 
without even a tentative claim to be a fact.i The other two correspond 
to the two great types of problem, in which either the major or the minor 
premise is in question; for the difficulty in a situation that needs clear- 
ing up may lie primarily in the need either of constructing or of selecting 
a concept, the concept standing for the mode of interpretation which we 
carry over from one experience to another. While Mill's classification 
of hypotheses and his selection of examples are somewhat confused in 
detail, it is at least clear that hypothesis has its place in the clearing up 
of any problematic situation; it is not limited to the discovery of uni- 
versal propositions only. 

' 349(^. Cf . Hobhouse, Theory of Knowledge, 418. 

' 349<^- ^ 3596-60. 

'^ iSS'^S^O'- Cf. 3Si(^-S3&. 



46 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

However broad their service in leading over from some facts to others, 
in their inner character they seem for Mill to be made of a different sort 
of stuff from the facts which they are intended to explain or by which 
they are tested. But is not this to misunderstand the character of these 
facts ? On the one hand, if we had the facts at the start there would be 
no occasion for any hypothesis and none would arise. It is because in 
some respect the "facts" have failed us that we are compelled to attempt 
a reconstruction, and our reconstruction at any stage is the nearest 
available approach to the facts. If not fact, the hypothesis is the most 
active possible candidate for that title. When a hypothesis becomes 
fact, it does not change its inner nature; it simply does its work so well 
that it satisfies.^ It is idle, therefore, to treat the facts as already given, 
and the hypothesis as a structure of our own somehow additional to the 
facts; for we get hold of the facts only as some interpretation of them 
obtains justification by satisfactorily clearing them up. The interpre- 
tation provides the facts quite as truly as the facts suggest the inter- 
pretation; because the facts for us are always the facts as we interpret 
them, and our interpretation is always the best statement we can offer, 
under the circumstances, of what the facts really are. So, on the other 
hand, the proof of a hj^othesis is not the external and accidental bring- 
ing of it to the test of facts which are ahen to its nature and which would 
remain untouched by its own fate. Mill employs no little ingenuity in 
explaining why a legitimate hypothesis must be capable of proof by 
"independent evidence." Is it not simply that if the hypothesis has 
done its work the facts to which it brings us must be different from the 
"facts" from which it set out, else these would never have needed the 
reinterpretation ? 

Mill distinguishes hypotheses which can be proved from those which 
can only be disproved. "We want to be assured that the law we have 
hypothetically assumed is a true one; and its leading deductively to true 
results will afford this assurance, provided the case be such that a false 
law cannot lead to a true result; provided no law, except the very one 
which we have assumed, can lead deductively to the same conclusions 
which that leads to. And this proviso is often realized."^ But it is 
realized only inside of a larger system which for the purpose of the 
inquiry need not be questioned, but is of the same essential character 
as that of the interpretation within the system. Alternatives which at 
one stage of an investigation or one period of human knowledge seem to 

' Sidgwick, The Process of Argument, 12-21, makes an acute analysis of the relation 
of fact and inference, and shows it to be one of degree. 



INFERENCE AS DISCOVERY 47 

be absolute mutual exclusives, cease later to be such through a revision 
of the system within which they fall. In contrast to the hypothesis that 
can be definitely proved, Mill considers such hypotheses as that of 
Descartes' celestial vortices, which "could not lead to any course of 
investigation capable of converting it from an hypothesis into a proved 

fact. It might chance to be disproved Direct evidence of its 

truth there could not be."^ In principle, however, there is no diEference; 
all proof is disproof. There is every difference in the degree to which 
the disproof of one interpretation is felt to be a satisfactory proof of 
another, but there is never another kind of proof than that. The move- 
ment of inference is positive, not negative; and any bona fide interpre- 
tation of the facts has a right to hold the field till it meets with obstacles 
and is challenged by a better. 

There seems to be no escape for Mill from an ex post facto view of 
"facts." After an inference has done its work we can then look back 
upon the facts as the inference has now interpreted them, and our 
rejected or outworn hypotheses we set up in contrast to the facts and 
call them errors. This ex post facto attitude is the temptation always 
waiting in the path of the realist, as Mill must be classed in this part of 
his theory. The very word "fact" plays into his hands.^ For common 
purposes we very properly confine attention to the results of our infer- 
ences, and forget the process of the inference, as we might kick out a 
ladder when we have climbed to our goal. We then speak of the facts 
at an earlier stage as we now at a later stage know them to have been, 
which is legitimate from the point of view of the later stage, but illegiti- 
mate if we shift the point of view to a consideration of the inference as it 
took place at the earlier stage. Mill exemplifies this shift when, in con- 
nection with the passage just quoted, he says of the vortices of Descartes, 
that "the hypothesis would have been false, though no such direct evi- 
dence of its falsity had been procurable. "^ Here the shift of standpoint 
is surely obvious. But precisely the same shift, though in more subtle 
guise, is involved in the assumption that definite, accepted facts are at 
hand both to prompt and to test hypotheses.'' 

' 3SS0- 

' "It is impossible to bring one's beliefs into harmony with facts, except so far as 
the facts are known to us" (Joseph, Introduction to Logic, 344). 

' 355a. 

* Mill commits the same fallacy when he seriously maintains that if one asserts 
a general proposition he has thereby actually asserted every case, including those 
then unknown, that may ever come under it (141a and note). This is to occupy an 
assumed point of view, not merely of the "innocent bystander," but of an absolute 
bystander. 



48 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

This would seem to afford an explanation also of Mill's repeated con- 
troversy with Whewell regarding the difference between colligation of 
facts and induction. It is an ex post facto distinction. An induction, 
Mill holds, must be either true or false, while a mere colligation need not 
be either.' But many an alleged induction has proved later to have 
been a colligation in Mill's sense. Mill admits that the colligation is 
"not the sum of the observations merely," but is " the sum of the observa- 
tions seen under a new point of view" ; but claims that "a real induction 
is ... . the sum of more than the observations."^ But this is to forget 
that a new point of view is more, in the sense of a reconstruction, a better 
grasp of the facts, and that a real induction adds a general law to the 
facts only in the sense of knowing them better. The general law has no 
existence whatever outside the facts, if we remember that the only facts 
we can speak of are the facts as we take them. But as we look back 
upon our inferences we distinguish the constructions made from a dis- 
carded "point of view" and those which still hold good; the one we then 
may very well consider a colligation of the facts under a descriptive con- 
ception, the other we consider the addition of real law. 

It is possible in the same way to explain Mill's contention regarding 
the origin of our "conceptions," which is simply the question of whence 
our hypotheses arise. Mill, iri defense of empiricism, set out boldly with 
the assertion that "the conceptions .... which we employ for the 
colligation and methodization of facts, do not develop themselves from 
within, but are impressed upon the mind from without," and that they 
are usually obtained by comparison and abstraction "from the very 
phenomena which it is their office to colligate."^ Mill is quite right here 
as against the extreme a priori position of Whewell. But the concep- 
tion we use is after all a function of our previous experience and of the 
whole situation, the hypothesis being tentatively taken and the situation 
gradually cleared up. Mill goes on, in very different terms from those 
just quoted, to describe the process by which "we advance from a less 
to a more appropriate general conception, in the progress of our investi- 
gations";'' the process in which the conception is alternately "furnished 
to the mind" and "furnished by the mind." "In endeavoring to arrange 
the facts, at whatever point we begin, we never advance three steps witti- 
out forming a general conception, more or less distinct and precise; and 
.... this general conception becomes the clue which we instantly 
endeavor to trace through the rest of the facts." "If we are not satis- 
fied with the agreements which we discover among the phenomena" by 

'218-19. ^ 22id. 3427c. •'463c. 



INFERENCE AS DISCOVERY 49 

using this conception, "we change our path, and look out for other 
agreements." "The different conceptions which the mind successively 
tries, it either already possessed from its previous experience, or they 
were supplied to it in the first stage of the corresponding act of compari- 
son."' This tentative process can be defined only in terms of the 
mutually constitutive relation of hypotheses and facts. 

Still less can Mill maintain that the contribution between hj^othesis 
and fact is all in one direction when he explains what is meant by "appro- 
priate" conceptions. "The question of appropriateness is relative to 
the particular object we have in view."^ " Some modes of classing things 
are more valuable than others for human uses, whether of speculation or 
of practise; and our classifications are not well made, unless the things 
which they bring together .... agree with each other and differ from 
other things in the very circumstances which are of primary importance 
for the purpose .... which we have in view, and which constitutes 
the problem before us." Our conceptions must "help us toward what 
we wish to understand."^ But, now, what is the criterion of such appro- 
priateness ? The answer is suggested by Mill, though he by no means 
appreciates its full significance. " That the conception we have obtained 
is the one we want, can only be known when we have done the work for 
the sake of which we wanted it; when we completely understand .... 
the phenomena .... with which we concern ourselves." But "pre- 
mature conceptions we must be continually making up, in our progress 
to something better. They are an impediment to the progress of knowl- 
edge, only when permanently acquiesced in."'^ The "work to be done" 
by the hypothesis is to give us the very facts which we can then, if there 
is occasion so to do, assume to have been present before the hypothesis 
was suggested. We are entirely justified in reading them back in this 
way from the later point of view after we have reached it, and so long 
as we maintain it; but we could not have held this point of view, or 
grasped the facts which we thus read back, if the hypothesis had not 
done its work. 

The cardinal error, then, of Mill's theory of inference is to read back 
the results of inference so as to make it seem to operate upon completely 
determined fact. The facts on which inference is supposed to be based, 
and to which it is expected to apply, whether these are regarded as the 
ultimate mental constituents of associational psychology or the things 
and events of objective naturalism, are by Mill all equally taken to be 
the sort of definitely determined realities such as they can be known to 



50 RELATION OF INFERENCE TO FACT IN MILL'S LOGIC 

be only after inference has in any case done its work. Facts when thus 
determined are found to possess attributes whose universal and system- 
atic character betrays their origin in the reflectively interpretative con- 
structions of experience. In passing from one fact of this kind to another 
there is no place found for a living act of inference, because the work 
which inference should do has already been assumed, and inference col- 
lapses into a formal relation within simultaneously presented contents. 
While a subsidiary place must finally be left open for invention and dis- 
covery, these are not assigned by Mill any constitutive function in the 
determining of the facts which were given in the first place. Fact and 
inference therefore fall apart, and in trying to find a vital relation between 
them Mill oscillates from one to the other. His difficulties could be 
removed only by recognizing the ultimate unity of inference and fact, 
and developing their distinction only as an instrumental function in the 
process of knowledge. 



